Place each chicken breast between two pieces of plastic wrap and pound to an even 1/2-inch thickness using a meat mallet or rolling pin.

Season the flour with salt and pepper on a shallow plate and dredge each chicken breast, shaking off excess.

Heat the olive oil in a large skillet over medium-high heat until shimmering.

Cook the chicken breasts for 3-4 minutes per side, until golden brown and cooked through, then remove and set aside.

Add the butter to the skillet and melt over medium heat.

Stir in the chicken broth, lemon juice, and capers, scraping up any browned bits from the pan.

Bring the sauce to a simmer and cook for 3-4 minutes, until slightly thickened, then season with salt and pepper.

Return the chicken to the skillet, spoon the sauce over each piece, and cook for 1 more minute to heat through.

Transfer the chicken to a serving platter, pour the sauce over the top, and garnish with chopped parsley before serving.